Results 21 to 30 of about 5,148,909 (356)
Universal Differential Equations for Scientific Machine Learning [PDF]
arXiv.org, 2020 In the context of science, the well-known adage “a picture is worth a thousand words” might well be “a model is worth a thousand datasets.” Scientific models, such as Newtonian physics or biological gene regulatory networks, are human-driven ...
Christopher Rackauckas +7 more
semanticscholar +1 more source
FOURIER PROBLEM FOR WEAKLY NONLINEAR EVOLUTION INCLUSIONS WITH FUNCTIONALS
Journal of Optimization, Differential Equations and Their Applications, 2019 The Fourier problem or, in other words, the problem without initial conditions for evolution equations and inclusions arise in modeling different nonstationary processes in nature, that started a long time ago and initial conditions do not affect on them
Mykola M. Bokalo, Iryna V. Skira
doaj +1 more source
Asymptotic Stability of Solutions to a Class of Second-Order Delay Differential Equations
Mathematics, 2021 We consider a class of second-order nonlinear delay differential equations with periodic coefficients in linear terms. We obtain conditions under which the zero solution is asymptotically stable. Estimates for attraction sets and decay rates of solutions
Gennadii V. Demidenko +1 more
doaj +1 more source
DIFFERENTIAL EQUATIONS ON GRAPHS [PDF]
Mathematics of the USSR-Sbornik, 1972 Summary: The differential equations encountered in various applications may be treated as equations on graphs. In the paper it is shown that the structure of the graph allows us to investigate the properties of the solutions of such equations.
openaire +2 more sources
Ordinary Differential Equations [PDF]
, 2021 AbstractIn this chapter, we discuss a first application of the time derivative operator constructed in the previous chapter. More precisely, we analyse well-posedness of ordinary differential equations and will at the same time provide a Hilbert space proof of the classical Picard–Lindelöf theorem (There are different notions for this theorem.
Christian Seifert +2 more
openaire +1 more source
DeepXDE: A Deep Learning Library for Solving Differential Equations [PDF]
AAAI Spring Symposium: MLPS, 2019 Deep learning has achieved remarkable success in diverse applications; however, its use in solving partial differential equations (PDEs) has emerged only recently.
Lu Lu +3 more
semanticscholar +1 more source
Constructive method for solvability of Fredholm equation of the first kind
Electronic Journal of Qualitative Theory of Differential Equations, 2017 The solvability and construction of the general solution of the first kind Fredholm integral equation are among the insufficiently explored problems in mathematics. There are various approaches to solve this problem.
Serikbai Aisagaliev, Zhanat Zhunussova
doaj +1 more source
Controlled K-Fusion Frame for Hilbert Spaces
Moroccan Journal of Pure and Applied Analysis, 2021 K-fusion frames are a generalization of fusion frames in frame theory. In this paper, we extend the concept of controlled fusion frames to controlled K-fusion frames, and we develop some results on the controlled K-fusion frames for Hilbert spaces, which
Assila Nadia +2 more
doaj +1 more source
The Cauchy Problem for Parabolic Equations with Degeneration
Advances in Mathematical Physics, 2020 Annotation. For a second-order parabolic equation, the multipoint in time Cauchy problem is considered. The coefficients of the equation and the boundary condition have power singularities of arbitrary order in time and space variables on a certain set ...
Ivan Pukal’skii, Bohdan Yashan
doaj +1 more source
Differential Equations in Fréchet Differentials Occurring in Integral Equations [PDF]
Proceedings of the National Academy of Sciences, 1945 Not ...
openaire +2 more sources